Borehole Compensation During Pulsed-Neutron Porosity Logging

ABSTRACT

Methods, tools, and systems for determining porosity in an earth formation are disclosed. Neutrons are emitted into the formation to induce inelastic scattering gamma rays and thermal capture gamma rays in the formation. The induced gamma rays are detected at a proximal gamma detector and a far gamma detector, which are spaced at different axial distances from the neutron source. A measured proximal-to-far inelastic ratio (a ratio of inelastic scattering gammas detected at the proximal and far detector) and a proximal-to-far thermal capture ratio (a ratio of thermal capture gammas detected at the proximal and far detector) are determined and used to calculate the formation porosity. Techniques are disclosed for removing borehole and casing configuration effects from the measured proximal-to-far thermal capture ratio, leaving only porosity dependence.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. Non-Provisional applicationSer. No. 16/584,318, filed Sep. 26, 2019, which is a Non-Provisional ofU.S. Provisional Application Ser. No. 62/832,061, filed Apr. 10, 2019.Both of these applications are incorporated herein by reference, andpriority is claimed to both.

FIELD OF THE INVENTION

The present application relates to logging of boreholes in oil and gasoperations, and more particularly, to pulsed-neutron porosity logging.

INTRODUCTION

Oil and gas wells can extend thousands of feet below the earth's surfaceand can traverse many geological formations. Such wells can includesections that are essentially vertical, segments that are essentiallyhorizontal, and transitions between the two. Because of the enormouscosts involved in drilling and completing oil and gas wells, it isimperative that the wells meet expectations in terms of hydrocarbonproduction.

Oil and gas well service providers use a variety of measurements todetermine if wells are producing to their potential, if they aremaintaining their integrity, and if interventions are needed to improveproduction or to otherwise repair or rejuvenate aging wells. Pulsedneutron measurements are one type of measurement available to wellservice providers. Pulsed neutron measurements can be used to identifyoil and gas in geological formations, evaluate hydrocarbon production,characterize the porosity of formations, and determine the condition ofcertain features of a well, such as gravel pack density.

A well service provider uses a tool called a pulsed neutron logging toolto perform pulsed neutron measurements. FIG. 1 illustrates a section ofa wellbore 100 extending into a formation 101. The illustrated wellbore100 is stabilized by a casing 103 held against the formation 101 bycement 104. The cylindrical volume 102, which is that part of thewellbore located inside the inner radius of the casing annulus, isfilled with a borehole fluid or gas. Tubing may also be present, but isnot shown here. Note that the methods and tools described in thisdisclosure are not limited to cased wellbores and may be used in openhole applications as well. A pulsed neutron logging tool 105 is loweredinto the cylindrical volume 102 using a wireline 106. The pulsed neutronlogging tool 105 includes a neutron generator nG, and one or moredetectors, labeled here as ND (near detector) and FD (far detector) inFIG. 1. Each component will be described in more detail below.

During a pulsed neutron measurement, the neutron generator nG generatesneutrons, which are released from the pulsed neutron logging tool 105 atgreater than 1 MeV and typically about 14 MeV. The neutrons arerepresented as straight arrows labeled n in FIG. 1. The high-energyneutrons can undergo a variety of interactions with matter in thecylindrical volume 102, the casing 103, the cement 104, and theformation 101.

FIG. 2 illustrates three types of such interactions. One possibleinteraction is an elastic collision, also called elastic scattering,between a neutron n and a nucleus. In the illustrated example, theneutron n collides with a hydrogen nucleus, which consists of a singleproton p. Hydrogen is omnipresent in most formations due to the porespaces being filled with liquid hydrocarbons or water. In the elasticscattering process, the neutron n imparts some of its energy to theproton p, causing the proton to gain energy and the neutron to loseenergy (i.e., to slow down). Since hydrogen is very light, it absorbs alarge fraction of the neutron energy in each scattering, and plays amajor role in the slowing down of fast neutrons. It is well known in theart that the liquid-filled porosity can be inferred by measuring theslowing down distance of fast neutrons.

In an inelastic collision, also called inelastic scattering, a neutroncollides with a nucleus, imparting a portion of the neutron's energy tothe nucleus. The neutron exits the collision with less energy thanbefore. The energy that is transferred to the nucleus excites thenucleus, which subsequently emits a gamma (γ) photon when the nucleusrelaxes. Nuclei of different atoms emit gamma photons having differentenergies. Therefore, the energy of the emitted gamma photon isindicative of the type of nucleus involved in an inelastic collision.For example, one can determine the ratios of carbon (indicative ofhydrocarbons), oxygen (indicative of water), silicon (indicative ofsandstone), and calcium (indicative of limestone) by measuring theenergies of gamma photons generated during inelastic collisions withatoms of those substances near a wellbore.

Notice that both elastic and inelastic scattering cause neutrons to loseenergy. After a high energy neutron has undergone a number ofcollisions, its energy-will be reduced. Neutrons having an energy aboveapproximately 1 MeV are considered fast neutrons. Fast neutrons cantrigger gamma rays due to inelastic scattering, as described above.Neutrons that are slowed to about 0.4 to 100 eV are considered“epithermal neutrons” and neutrons that are slowed to about 0.025 eV arereferred to as “thermal neutrons.” Epithermal and thermal neutrons canparticipate in a third type of interaction whereby the thermal neutronis “captured” by the nucleus of an atom. The capturing nucleus becomesexcited and emits a gamma photon when it relaxes. The nuclei of someatoms have a greater affinity to capture thermal neutrons than othernuclei.

As mentioned above, pulsed neutron measurements can be used to measureformation porosity. Such measurements are based on the fact that theslowing down of neutrons, and therefore the average distance travelledwithin the formations by the neutrons, is strongly dependent on thehydrogen content of the formation (i.e., hydrogen within the pore spacesof the formation). The hydrogen content dependency is due to the factthat neutrons can incur a very large energy loss in a single elasticscattering event with a proton (a hydrogen nucleus). However, suchporosity measurements are strongly affected by the borehole environment(e.g. borehole fluid, casing configuration).

U.S. Pat. No. 10,001,582 describes a method for determining anenvironmentally corrected porosity of a formation that includesdetecting gamma rays at two different positions from a position of asource of neutrons emitted neutrons into the formation at an energylevel sufficient to induce inelastic scattering gamma rays. The neutronsare emitted in a plurality of bursts of neutrons into the formation, thebursts each having a first selected duration. Each burst is followed bya wait time having a second selected duration, the gamma rays beingdetected during each of the bursts and each of the wait times. A ratioof numbers of gamma rays detected during the bursts is determined (burstratio). A ratio of numbers of gamma rays detected during the wait timesis determined (capture ratio). The burst ratio is used to correct thecapture ratio. The environmentally corrected porosity is determined fromthe corrected capture ratio.

U.S. Pat. No. 9,995,842 describes a method for determining anenvironmentally corrected porosity that includes using measurements ofgamma rays detected during operation of a pulsed neutron source andnumbers of burst and thermal neutron capture gamma rays made at twodifferent axial spacings from a pulsed neutron source. Theenvironmentally corrected porosity is calculated from a correctedcapture ratio which is a function of either the burst ratio, captureratio and capture/burst ratio or just the burst ratio and capture ratio.

The inventors have found that the prior art methods of compensating forborehole environment are strongly dependent on the capabilities of thelogging tool, in particular, the burst width. Thus, there is a need inthe art for more generally applicable methods of improving pulsedneutron measurements by correcting for borehole effects.

SUMMARY

Disclosed herein is a method of measuring a porosity of an earthformation traversed by a wellbore. According to some embodiments, themethod comprises: receiving data generated by a logging tool, whereinthe logging tool comprises: a neutron source configured to emit neutronsinto the formation at an energy sufficient to induce inelasticscattering gamma rays and thermal capture gamma rays in the formation, aproximal gamma detector spaced a first axial distance from the neutronsource, and a far gamma detector spaced a second axial distance from theneutron source. According to some embodiments, the data indicates totalgamma rays detected at the proximal gamma detector and total gamma raysdetected at the far gamma detector. According to some embodiments, themethod comprises: determining a count of thermal capture gamma raysdetected at the proximal gamma detector and a count of thermal capturegamma rays detected at the far gamma detector. According to someembodiments, the method comprises: determining a count of inelasticscattering gamma rays detected at the proximal gamma detector and acount of inelastic scattering gamma rays detected at the far gammadetector. According to some embodiments, the method comprises:determining a proximal-to-far thermal capture ratio as a ratio of thecount of thermal capture gamma rays detected at the proximal gammadetector to the count of thermal capture gamma rays detected at the fargamma detector. According to some embodiments, the method comprises:determining a proximal-to-far inelastic ratio as a ratio of the count ofinelastic scattering gamma rays detected at the proximal gamma detectorto the count of inelastic scattering gamma rays detected at the fargamma detector. According to some embodiments, the method comprises:using the proximal-to-far thermal capture ratio and the proximal-to-farinelastic ratio to determine the porosity.

According to some embodiments, the data indicating the total gamma raysdetected at the proximal gamma detector and the total gamma raysdetected at the far gamma detector comprises, for each detector, a timespectrum indicating gamma ray counts detected at the detector as afunction of time, wherein each time spectrum comprises a burst intervalindicating gamma ray counts detected while the neutron source isemitting neutrons and a decay interval indicating gamma ray countsdetected while the neutron source is not emitting neutrons. According tosome embodiments, determining the count of thermal capture gamma raysdetected at the proximal gamma detector and the count of thermal capturegamma rays detected at the far gamma detector comprises, for each of theproximal gamma detector and the far gamma detector: determining a countof thermal capture gamma rays detected during the decay interval at thatdetector, and determining a count of thermal capture gamma rays detectedduring the burst interval at that detector. According to someembodiments, determining a count of thermal capture gamma rays detectedduring the decay interval comprises integrating the time spectrum overthe decay interval. According to some embodiments, determining a countof thermal capture gamma rays detected during the burst intervalcomprises: fitting a decay function to the decay interval of the timespectrum, determining a borehole component and a formation component ofthe decay function over the decay interval, convolving the boreholecomponent and the formation component of the decay function over theburst interval, and summing the convolved borehole component and theconvolved formation component over the burst interval to determine thecount of thermal capture gamma rays detected during the burst interval.According to some embodiments, the decay function is a dual exponentialfunction. According to some embodiments, determining a count ofinelastic scattering gamma rays detected at the proximal gamma detectorand a count of inelastic scattering gamma rays detected at the far gammadetector comprises, for each detector, subtracting the count of thermalcapture gamma rays detected during the burst interval from the totalgamma rays detected during the burst interval. According to someembodiments, using the proximal-to-far thermal capture ratio and theproximal-to-far inelastic ratio to determine the porosity comprisesapplying a correction function to the proximal-to-far thermal captureratio to determine a corrected proximal-to-far capture ratio that isindependent of borehole and casing configuration effects, wherein thecorrection function is a function of the proximal-to-far thermal captureratio and the proximal-to-far inelastic ratio. According to someembodiments, the correction function is determined based on a pluralityof calibration proximal-to-far ratios determined by modeling responsesof the logging tool response under a plurality of modeled formationconditions. According to some embodiments, the correction function isdetermined based on a plurality of calibration proximal-to-far ratiosdetermined by measuring responses of the logging tool to a plurality ofcalibration formation conditions. According to some embodiments, themethod further comprises deploying the logging tool in the borehole andacquiring the data.

Also disclosed herein is a system for measuring a porosity of an earthformation traversed by a wellbore, the system comprising a logging toolcomprising: a neutron source configured to emit neutrons into theformation at an energy sufficient to induce inelastic scattering gammarays and thermal capture gamma rays in the formation, a proximal gammadetector spaced a first axial distance from the neutron source, and afar gamma detector spaced a second axial distance from the neutronsource. The system further comprises a computer configured to: receivedata generated by the logging tool, wherein the data indicates totalgamma rays detected at the proximal gamma detector and total gamma raysdetected at the far gamma detector, from the data, determine a count ofthermal capture gamma rays detected at the proximal gamma detector and acount of thermal capture gamma rays detected at the far gamma detector,from the data, determine a count of inelastic scattering gamma raysdetected at the proximal gamma detector and a count of inelasticscattering gamma rays detected at the far gamma detector, determine aproximal-to-far thermal capture ratio as a ratio of the count of thermalcapture gamma rays detected at the proximal gamma detector to the countof thermal capture gamma rays detected at the far gamma detector,determine a proximal-to-far inelastic ratio as a ratio of the count ofinelastic scattering gamma rays detected at the proximal gamma detectorto the count of inelastic scattering gamma rays detected at the fargamma detector, and determine the porosity from the proximal-to-farthermal capture ratio and the proximal-to-far inelastic ratio. Accordingto some embodiments, the data indicating the total gamma rays detectedat the proximal gamma detector and the total gamma rays detected at thefar gamma detector comprises, for each detector, a time spectrumindicating gamma ray counts detected at the detector as a function oftime, wherein each time spectrum comprises a burst interval indicatinggamma ray counts detected while the neutron source is emitting neutronsand a decay interval indicating gamma ray counts detected while theneutron source is not emitting neutrons. According to some embodiments,determining the count of thermal capture gamma rays detected at theproximal gamma detector and the count of thermal capture gamma raysdetected at the far gamma detector comprises, for each of the proximalgamma detector and the far gamma detector: determining a count ofthermal capture gamma rays detected during the decay interval at thatdetector, and determining a count of thermal capture gamma rays detectedduring the burst interval at that detector. According to someembodiments, determining a count of thermal capture gamma rays detectedduring the decay interval comprises integrating the time spectrum overthe decay interval. According to some embodiments, determining a countof thermal capture gamma rays detected during the burst intervalcomprises: fitting a decay function to the decay interval of the timespectrum, determining a borehole component and a formation component ofthe decay function over the decay interval, convolving the boreholecomponent and the formation component of the decay function over theburst interval, and summing the convolved borehole component and theconvolved formation component over the burst interval to determine thecount of thermal capture gamma rays detected during the burst interval.According to some embodiments, the decay function is a dual exponentialfunction. According to some embodiments, determining a count ofinelastic scattering gamma rays detected at the proximal gamma detectorand a count of inelastic scattering gamma rays detected at the far gammadetector comprises, for each detector, subtracting the count of thermalcapture gamma rays detected during the burst interval from the totalgamma rays detected during the burst interval. According to someembodiments, using the proximal-to-far thermal capture ratio and theproximal-to-far inelastic ratio to determine the porosity comprisesapplying a correction function to the proximal-to-far thermal captureratio to determine a corrected proximal-to-far capture ratio that isindependent of borehole and casing configuration effects, wherein thecorrection function is a function of the proximal-to-far thermal captureratio and the proximal-to-far inelastic ratio. According to someembodiments, the correction function is determined based on a pluralityof calibration proximal-to-far ratios, wherein the plurality ofcalibration proximal-to-far ratios is determined by one or more of:modeling responses of the logging tool response under a plurality ofmodeled formation conditions, and measuring responses of the loggingtool to a plurality of calibration formation conditions.

Also disclosed herein is a method of measuring a porosity of an earthformation traversed by a wellbore, the method comprising receiving datagenerated by a logging tool, wherein the logging tool comprises: aneutron source configured to emit neutrons into the formation at anenergy sufficient to induce inelastic scattering gamma rays and thermalcapture gamma rays in the formation, a proximal gamma detector spaced afirst axial distance from the neutron source, and a far gamma detectorspaced a second axial distance from the neutron source. According tosome embodiments, the data indicates total gamma rays detected at theproximal gamma detector and total gamma rays detected at the far gammadetector. According to some embodiments, the method comprises: from thedata, determining a count of thermal capture gamma rays detected at theproximal gamma detector and a count of thermal capture gamma raysdetected at the far gamma detector, determining a proximal-to-farthermal capture ratio as a ratio of the count of thermal capture gammarays detected at the proximal gamma detector to the count of thermalcapture gamma rays detected at the far gamma detector, determining aborehole thermal neutron capture cross section, and using theproximal-to-far thermal capture ratio and the borehole thermal neutroncapture cross section to determine the porosity. According to someembodiments, the data indicating the total gamma rays detected at theproximal gamma detector and the total gamma rays detected at the fargamma detector comprises, for each detector, a time spectrum indicatinggamma ray counts detected at the detector as a function of time, whereineach time spectrum comprises a burst interval indicating gamma raycounts detected while the neutron source is emitting neutrons and adecay interval indicating gamma ray counts detected while the neutronsource is not emitting neutrons. According to some embodiments,determining the count of thermal capture gamma rays detected at theproximal gamma detector and the count of thermal capture gamma raysdetected at the far gamma detector comprises, for each of the proximalgamma detector and the far gamma detector: determining a count ofthermal capture gamma rays detected during the decay interval at thatdetector, and determining a count of thermal capture gamma rays detectedduring the burst interval at that detector. According to someembodiments, determining a count of thermal capture gamma rays detectedduring the decay interval comprises integrating the time spectrum overthe decay interval. According to some embodiments, determining a countof borehole thermal capture gamma rays detected during the decayinterval comprises: fitting a decay function to the decay interval ofthe time spectrum, and determining a borehole component and a formationcomponent of the decay function over the decay interval. According tosome embodiments, the decay function is a dual exponential function(DEF). According to some embodiments, the dual exponential function(DEF) is expressed as: DEF=A_(BH)*exp(−t/τ_(F)), where A_(BH) and A_(F)are coefficients, t is time, τ_(BH) is a borehole decay constant, andτ_(F) is a formation decay constant. According to some embodiments, theborehole thermal neutron capture cross section is determined based onτ_(BH).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a logging tool according to the prior art.

FIG. 2 shows interactions of fast neutrons according to the prior art.

FIG. 3 shows an embodiment of a logging tool according to aspects of thedisclosure.

FIG. 4 shows a temporal profile of gamma ray count rate at a detector.

FIG. 5 shows a plot of porosity as a function of the Prox/Far thermalcapture ratio for a liquid-filled borehole.

FIG. 6 shows an embodiment for correcting a porosity measurement toaccount for borehole/casing configuration effects, according to aspectsof the disclosure.

FIGS. 7A-7C show processing of a temporal profile of gamma ray countrate to determine contributions of inelastic scattering and thermalcapture.

FIGS. 8A-8B show correction for epithermal neutron capture.

FIG. 9 shows MCNP simulated Prox/Far (P/F) inelastic and capture ratiosfor three different porosities, and various different boreholefluid/casing configurations, in a limestone formation.

FIGS. 10A-10C show the process for experimentally determining a boreholecorrection for the Prox/Far capture ratio.

FIG. 11 shows a time log in a sandstone block for three differentborehole environments: OH Air, OH FW, and CH FW.

FIG. 12 shows MCNP simulated Prox/Far capture ratios plotted against theborehole sigma value a limestone formation.

DESCRIPTION

FIG. 3 shows the layout of a typical pulsed neutron logging tool 300according to the disclosure. Subsection 302 houses an array of detectorassemblies as well as a pulsed neutron generator 304. More specifically,there are four detector assemblies in the illustrated embodiment, eachcomprising a LaBr₃ crystal coupled to a photomultiplier tube and adigital spectrometer for filtering and pulse inspection. These detectorassemblies are referred to as the Proximal (Prox) detector assembly 306,the Near detector assembly 308, the Far detector assembly 310, and Longdetector assembly 312. These detector assemblies are disposed atincreasing axial spacings from the neutron generator 304, as their namesimply. Between the near detector assembly 308 and the far detectorassembly 310 is disposed a fast neutron detector 314 that measures thefast neutron flux.

The subsection 302 is operationally connected to an instrumentsubsection 316. The instrument subsection houses control circuits andpower circuits to operate and control the elements of the subsection302. A telemetry subsection 318 is operationally connected to theinstrument section 316. A suitable connector connects the logging toolto a lower end of a preferably multiconductor logging cable 320. Theupper end of the logging cable 320 terminates at a draw works, which iswell known in the art and is not shown in the illustration. It should benoted that other embodiments of a logging tools are within the scope ofthe disclosure. For example, the illustrated embodiment is an example ofa tool configured to be conveyed into a wellbore via a cable, such aslogging cable 320. However, other embodiments may be included as a partor subsection of other conveyed components, for example, as part of adrilling string for LWD/MWD applications. Moreover, although shownembodied in a wireline logging tool, the detector assembly 302 can alsobe embodied in other borehole instruments. These instruments includepump-down (“memory”) instruments conveyed by drilling fluid flow,instruments conveyed by coiled tubing, instruments conveyed by a drillstring, and instruments conveyed by a “slick line”.

Still referring to FIG. 3, detector assembly response data aretelemetered from the tool 300 to the surface of the earth where they arereceived by an uphole telemetry unit (not shown) typically disposedwithin surface equipment. These data can be processed in a surfaceprocessor (not shown) within the surface equipment to yield a log of oneor more parameters of interest. Alternately, data can be partially orcompletely processed in a downhole processor, for example, within theinstrument section 316 and telemetered via the telemetry subsection 318to the surface equipment. Control parameters can also be telemeteredfrom the surface equipment to the tool 300 via the telemetry system andwireline cable 320.

FIG. 4 shows the temporal profile of the gamma ray count rate in one ofthe detectors (e.g., the near detector) during a pulsed neutronmeasurement. During the illustrated pulsed neutron measurement, theneutron generator generates neutrons during a burst lasting about 150μs. During the neutron burst the gamma rays detected include gamma raysgenerated by inelastic scattering, thermal capture, and epithermalcapture. Once the neutron burst is terminated, the detected gamma signalbegins to decay. For a very short time following the burst, gamma raysdue to epithermal and thermal neutron capture are detected, followed bya longer decay period during which all of the detected gammas arise fromthermal capture events.

It is known that the counting yield of each type of gamma ray reactionis sensitive to certain properties of the formation and/or properties ofthe wellbore. For example, porosity information can be obtained from ameasured capture ratio (i.e., the total capture decay counts in onedetector relative to another). FIG. 5 shows an example of aratio-to-porosity transform based on measured data and Monte Carlomodeling of the thermal capture ratio of the Proximal detector to theFar detector of a logging tool (FIG. 3).

However, it is important to note that the thermal capture ratio is alsosensitive to the borehole fluid and casing configuration. Therefore, inorder to obtain a porosity measurement that is sensitive solely to theformation, the borehole sensitivity must be accounted for.

This disclosure provides a new technique for removing the boreholesensitivity from the porosity measurement. The technique relies on theobservation that the inelastic ratio (e.g., the ratio of inelastic gammacounts measured at the Proximal detector to the inelastic gamma countsmeasured at the Far detector) is sensitive only to the borehole fluidand casing configuration and is not sensitive to formation porosity. Theinventors have discovered that the inelastic ratio can be used tocorrect for the borehole effects contained within the capture ratioporosity determination. By removing the borehole dependence from thecapture ratio, we are left with only the porosity dependence, which isthe desired measurement.

FIG. 6 illustrates the steps of an embodiment 600 of the disclosedmethod, at a high level. According to the illustrated embodiment, timespectra (such as shown in FIG. 4) are acquired at two detectors that areaxially spaced from one another 602. For example, referring to FIG. 3,the spectra could be acquired at the Prox detector 306 and Far detector310 of the logging tool 300. It should be noted, however, that otherdetectors could be used (e.g., any two detectors selected from theProximal detector 306, Near detector 308, Far detector 310, or the Longdetector 312, etc.). The point is that gamma counts are recorded at twodetectors axially spaced from one another so that ratios of the countscan be determined. For simplicity, such ratios will be referred toherein as Prox/Far ratios, even though it is understood that any twodetectors may be implicated.

Once the time spectra are acquired for the Prox and Far detectors, eachtime spectrum is processed to determine the contribution of inelasticcounts and thermal capture counts to the spectrum 604. Again, the reasonfor determining the contribution for each of the two processes isbecause inelastic scattering is influenced only by borehole/casingconfiguration effects, whereas thermal capture is influenced both byborehole/casing configuration effects and by formation porosity.Referring again to the time spectrum illustrated in FIG. 4, the decayregion following the burst is due solely to thermal capture events. So,determining the thermal capture counts for that region is simply amatter of integrating the area under the curve. However, the burstregion of the spectrum from 0 to 150 μs is indicative of both inelasticand thermal capture events. Thus, that region must be decomposed todetermine the counts resulting from each of those processes.

A method of decomposing the burst region to determine the contributionof inelastic counts and thermal capture counts is described withreference to FIGS. 7A-7C. In Step 1 of an exemplary embodiment shown inFIG. 7A, the decay capture region is fit with a dual-exponentialfunction:

Dual_exponential_function=A _(BH)*exp(−t/τ _(BH))+A _(F)*exp(−t/τ_(F))  (Eq-1)

where A_(BH) and A_(F) are the borehole and formation amplitudes, andτ_(BH) and τ_(F) are the borehole and formation decay time constants.According to some embodiments, the fitting can be performed in real timewith a weighted least-squares minimization technique. The result of thefitting is the amplitudes and decay time constants for both the boreholeand formation components of the thermal capture spectrum.

In Step 2 of the exemplary embodiment shown in FIG. 7B, the amplitudesand decay time constants from the dual-exponential fit are used todetermine the amount of thermal capture that occurs during the burstregion of the time spectrum. It should be noted that this is an inverseproblem, but can be solved exactly by convolving borehole and formationdecays over the burst window. This can be explained as follows. Theresults of the dual exponential fit to the decay region are amplitudesand decay times for the borehole (BH) and formation (F) decays. If wechoose the time variable, t, to start before the burst, we canre-express Eq.1 in the following form appropriate for the decay region(t_(DECAYSTART)<t<t_(DECAYEND)):

Decay Region

TC _(TOTAl)(t)=A _(BH,DECAYSTART)*exp(−(t−t _(DECAYSTART))/τ_(BH))+A_(F,DEVAYSTART)*exp(−(t−t _(DECAYSTART))τ_(F))  (Eq-2)

where TC_(TOTAL)(t) is the total thermal capture at time t,t_(DECAYSTART) is the time at the start of the decay window (whichfollows the burst window, t_(BURSTEND)), t_(DECAYEND) is the time at theend of the decay window (>1000 μS so as to allow a full decay),A_(BH,DECAYSTART) and A_(F,DECAYSTART) are the borehole and formationamplitudes at t_(DECAYSTART), and τ_(BH) and τ_(F) are the borehole andformation decay times.

For the burst region (t_(BURSTSTART)<t<t_(BURSTEND)), we can convolve anexponential function over the known width of the burst gate anddetermine a relationship between the strength of the convolvingexponential (TC_(BH) or TC_(F)) and the amplitude and decay times asdetermined during the dual-exponential fit of the decay region:

Burst Region

TC _(BH)(t)=A _(BH,DECAYSTART)*exp((t _(DECAYSTART) −t_(BURSTEND))τ_(BH))*(1−exp(−t/τ _(BH)))/1−exp(−t _(BURSTEND)/τ_(BH))),

TC _(F)(t)=A _(F,DECAYSTART)*exp((t _(DECAYSTART) −t_(BURSTEND))τ_(F))*(1−exp(−t/τ _(F)))/(1−exp(−t _(BURSTEND)/τ_(F))),

TC _(TOTAL)(t)=TC _(BH)(t)+TC _(F)(t)  (EQ.3)

where TC_(TOTAL)(t) is the total Thermal Capture at time t during theburst window (0 to 150 μs in the current examples).

Once Eq.3 is solved, the total thermal capture can then be subtractedfrom burst data in order to obtain an inelastic contribution:

I(t)=Burst(t)−TC _(TOTAL)(t)  (Eq.4)

where I(t) is the inelastic yield during the burst, and Burst(t) is themeasured data during the burst.

In Step 3 (FIG. 7C), the total thermal capture is subtracted from themeasured Data to generate the inelastic yield. The inelastic yieldobtained in the above manner does not account for epithermal effects.Although epithermal effects are usually small or entirely negligible,there are situations where they will be present (e.g. at small boreholesize and low porosity). In these cases, the epithermal will bemisidentified as inelastic, and the inelastic answer will appearslightly high. This can be corrected for as shown in FIGS. 8A and 8B.Since the dual exponential fit does not include the epithermal+thermalcapture window of FIG. 4, any residual I(t) strength in this window,after subtracting the Total Thermal Capture, is due to epithermalcapture. This will appear as a tail on the inelastic yield. The heightof the tail can be used to correct the inelastic yield for epithermalcapture. FIG. 8B shows the inelastic yield corrected based on the heightof the epithermal capture tail.

Referring again to FIG. 6, once each of the time spectra at each of thedetectors are decomposed into their respective inelastic and thermalcapture contributions, a ratio of inelastic counts for the Proximaldetector to the inelastic counts for the Far detector can be determined.Likewise, a ratio of thermal capture counts for the Proximal detector tothe thermal counts for the Far detector can be determined. In otherwords, Prox/Far ratios are determined for both the inelastic and thermalcounts 606.

Again, recall that the Prox/Far thermal capture ratio is a function ofthe formation porosity (as shown in FIG. 5), which is the parameter weseek to measure. However, the Prox/Far thermal capture ratio is alsosensitive to borehole/casing configuration effects, which can complicatethe porosity determination. Thus, the inventors have developedtechniques for using the Prox/Far inelastic ratio to correct forborehole/casing configuration effects that are included in the prox/farthermal capture ratio.

According to some embodiments, a correction function 608, based on theProx/Far inelastic ratio, is applied to the measured Prox/Far thermalcapture ratio to determine a “corrected Prox/Far capture ratio,” whichis independent of borehole/casing configuration effects and depends onlyon the formation porosity. The correction function is derived based on aset of “calibration Prox/Far values” that are determined either bymodeling (e.g., Monte Carlo N-Particle (MCNP) modeling) of the loggingtool or by performing laboratory measurements using the logging tool onknown samples. The derivation of the calibration Prox/Far values aredescribed below.

According to some embodiments, the calibration prox/far values aredetermined based on modeling the logging tool's responses under avariety of modeled borehole/casing configurations and porosities. Anexample of such modeling is Monte Carlo N-Particle (MCNP) modeling,which is familiar in the art (see, e.g., Cox, L. J. et al, MCNP version5, Los Alamos National Laboratory, Los Alamos, NM (2002)). To constructsuch a model, a temporal profile of the gamma ray count rates (i.e.,time spectra similar to FIG. 4) is modeled for a Prox and Far detectorof the tool under each of the borehole/casing configurations andporosities. Once the temporal gamma ray count rates (i.e., time spectra)for the detectors is determined (either by modeling or laboratorymeasurement) for a Prox and Far detector under each of the casingconfigurations and porosities, each of the time spectra are analyzed todetermine the inelastic counts and the thermal capture counts, asdescribed above in reference to FIGS. 7A-7C. This allows a determinationof a Prox/Far inelastic ratio and a Prox/Far thermal capture ratio foreach casing configuration and porosity. These determined Prox/Farinelastic ratios and a Prox/Far thermal capture ratios are referred toherein as the “calibration Prox/Far ratios.” The calibration Prox/Farinelastic and thermal capture ratios are used to derive a correctionfunction.

FIG. 9 illustrates calibration Prox/Far inelastic ratios cross plottedagainst calibration prox/far thermal capture ratios determined from MCNPmodeling of the logging tool response in water filled limestoneformations of porosities of 2, 18, and 25 pu. Curved lines connect therespective data at each porosity. The progression of the lines upwardsrepresents the increasing effective density of the borehole environment.The borehole fluid is seen to vary from lower density gas to higherdensity gas to fresh water (FW). The casing configuration is seen tovary from open-hole (OH) to single cased hole (CH) to double CH. Noticethat the calibration Prox/Far inelastic ratios are essentiallyindependent of porosity but are dependent on the borehole fluid andcasing configuration. However, the calibration prox/far thermal captureratios are dependent both on the borehole fluid/casing configuration andon the porosity.

The three curved lines in FIG. 9, which connect the points associatedwith each porosity, have nearly the same shape, but are shiftedhorizontally. To a good approximation, the slopes are similar, andnearly independent of porosity. This indicates that, to a goodapproximation, a given change in the P/F inelastic ratio, due to achange in borehole conditions, will result in a given change to the P/Fcapture ratio. This means that by measuring a change in the P/Finelastic ratio, we can determine a correction term for the P/F captureratio that will be applicable to all porosities.

FIGS. 10A-10C show a procedure to derive a correction function for theProx/Far capture ratio in the laboratory. FIG. 10A shows anexperimentally derived curve-fit from three measurements in a sandstoneblock. In each of the measurements, the borehole environment waschanged. The first measurement was for open-hole (OH) air, the secondmeasurement was for OH fresh water (FW), and the third measurement wasfor cased-hole (CH) FW. In FIG. 10B, the curve fit is inverted. Thedifference between the Prox/Far capture ratio in FW OH and the Prox/Farcapture ratio of the inverted curve-fit is then the correction functionthat can be applied, as an additive term, to the measured Prox/Farcapture ratio. FIG. 10C shows the correction function derived from FIG.10B. It is possible that the correction function plotted in FIG. 10Ccould be given a Prox/Far capture ratio dependence in order to make itslightly more accurate, but it should work as is to a goodapproximation.

For any measured prox/far thermal capture ratio, regardless of theborehole/casing configuration, the correction function allows one toextrapolate to a “corrected Prox/Far capture ratio.” The “correctedProx/Far capture ratio” is dependent only on porosity and is notdependent on the borehole/casing configuration. In other words, themeasured Prox/Far capture ratio is “corrected,” i.e., extrapolated to avalue corresponding to open hole conditions.

FIG. 11 shows an example of how the correction function of FIG. 10 wouldbe applied to a real log. This particular log is a time log of asandstone block with three different borehole conditions: OH Air, OH FW,and CH FW. In the left track, the measured Prox/Far inelastic andcapture ratios are shown by the dashed and dotted lines. On the righttrack, the uncompensated and compensated (i.e. uncorrected andcorrected) porosities are shown by the gray/dotted and black lines. Theuncorrected porosity varies greatly with the changing boreholeconditions, but the corrected porosity holds a steady line, as it shouldfor a block of fixed porosity.

The inventors have also discovered that borehole salinity can becompensated by plotting the borehole thermal neutron capture crosssection (i.e., the borehole sigma value, expressed in “capture units”)as a function of the P/F capture ratio, as shown in FIG. 12. Theborehole sigma value can be determined from the borehole decay timeconstant τ_(BH) from the dual-exponential fit (Eq. 1) and calculated asBorehole Sigma=4545/τ_(BH). In this equation, τ_(BH) is in microsecondsand the Borehole Sigma is in “capture units” (inverse decameters).Referring to FIG. 12, it can be seen that the borehole sigma is fairlyindependent of porosity, and only depends on the salinity of theborehole fluid as expressed in kppm. The P/F capture ratio, on the otherhand, is seen to be dependent upon both the porosity and the salinity ofthe borehole fluid. As such, the salinity dependence of the P/F captureratio can be removed by using the borehole sigma value.

In the same way that we used the P/F inelastic ratio in FIG. 9 to removethe borehole fluid density and casing effects from the P/F captureratio, we can also use the borehole sigma value to remove the salinityeffects. As shown in FIG. 12, the relationship between P/F capture ratioand borehole sigma, as expressed by the three curves, is approximatelythe same for each porosity—only a linear shift is involved. Thus, as wasthe case in FIG. 9 and FIG. 10, we can use the slope of the curve togive us a correction term to bring us back to FW OH conditions.

Some portions of the detailed description were presented in terms ofprocesses, methods, programs and workflows. These processes, methods,programs and workflows are the means used by those skilled in the dataprocessing arts to most effectively convey the substance of their workto others skilled in the art. A process or workflow is here, andgenerally, conceived to be a self-consistent sequence of steps(instructions) contained in memory and run using processing resources toachieve a desired result. The steps are those requiring physicalmanipulations of physical quantities. Usually, though not necessarily,these quantities take the form of electrical, magnetic or opticalsignals capable of being stored, transferred, combined, compared andotherwise manipulated. It has proven convenient at times, principallyfor reasons of common usage, to refer to these signals as bits, values,elements, symbols, characters, terms, numbers, or the like.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the following discussion,it is appreciated that throughout the description, discussions utilizingterms such as “processing,” “receiving,” “calculating,” “determining,”“displaying,” or the like, refer to the action and processes of acomputer system, or similar electronic computing device, thatmanipulates and transforms data represented as physical (electronic)quantities within the computer system memories or registers or othersuch information storage, transmission or display devices.

The present invention also relates to an apparatus for performing theoperations herein. This apparatus may be specially constructed for therequired purposes, or it may comprise a general-purpose computer,selectively activated or reconfigured by a computer program stored inthe computer. Such a computer program may be stored in a non-transitorycomputer readable storage medium, which could be, but is not limited to,any type of disk including floppy disks, optical disks, CD-ROMs, anmagnetic-optical disks, read-only memories (ROMs), random accessmemories (RAMs), EPROMs, EEPROMs, magnetic or optical cards, applicationspecific integrated circuits (ASICs), or any type of media suitable forstoring electronic instructions, and each coupled to a computer systembus. Furthermore, the computers referred to in the specification mayinclude a single processor, or may be architectures employing multipleprocessor designs for increased computing capability.

While the invention herein disclosed has been described in terms ofspecific embodiments and applications thereof, numerous modificationsand variations could be made thereto by those skilled in the art withoutdeparting from the scope of the invention set forth in the claims.

What is claimed is:
 1. A method of measuring a porosity of an earthformation traversed by a wellbore, the method comprising: receiving datagenerated by a logging tool, wherein the logging tool comprises: aneutron source configured to emit neutrons into the formation at anenergy sufficient to induce inelastic scattering gamma rays and thermalcapture gamma rays in the formation, a proximal gamma detector spaced afirst axial distance from the neutron source, and a far gamma detectorspaced a second axial distance from the neutron source, and wherein thedata indicates gamma rays detected at the proximal gamma detector andgamma rays detected at the far gamma detector, from the data,determining a count of thermal capture gamma rays detected at theproximal gamma detector and a count of thermal capture gamma raysdetected at the far gamma detector, determining a proximal-to-farthermal capture ratio as a ratio of the count of thermal capture gammarays detected at the proximal gamma detector to the count of thermalcapture gamma rays detected at the far gamma detector, determining aborehole thermal neutron capture cross section, and using theproximal-to-far thermal capture ratio and the borehole thermal neutroncapture cross section to determine the porosity.
 2. The method of claim1, wherein determining the porosity comprises using the borehole thermalneutron capture cross section to compensate for borehole salinity. 3.The method of claim 1, wherein the data indicating the gamma raysdetected at the proximal gamma detector and the gamma rays detected atthe far gamma detector comprises, for each detector, a time spectrumcomprising a burst interval indicating gamma ray counts detected whilethe neutron source is emitting neutrons and a decay interval indicatinggamma ray counts detected while the neutron source is not emittingneutrons.
 4. The method of claim 3, wherein determining the count ofthermal capture gamma rays detected at the proximal gamma detector andthe count of thermal capture gamma rays detected at the far gammadetector comprises, for each detector: determining a count of thermalcapture gamma rays detected during the decay interval at that detector,and determining a count of thermal capture gamma rays detected duringthe burst interval at that detector.
 5. The method of claim 4, whereindetermining a count of thermal capture gamma rays detected during thedecay interval comprises integrating the time spectrum over the decayinterval.
 6. The method of claim 4, wherein determining a count ofthermal capture gamma rays detected during the burst interval comprises:fitting a decay function to the decay interval of the time spectrum,determining a borehole component and a formation component of the decayfunction over the decay interval, convolving the borehole component andthe formation component of the decay function over the burst interval,and summing the convolved borehole component and the convolved formationcomponent over the burst interval to determine the count of thermalcapture gamma rays detected during the burst interval.
 7. The method ofclaim 1, wherein determining the borehole thermal neutron capture crosssection comprises: fitting a decay function to the decay interval of thetime spectrum, and determining a borehole component and a formationcomponent of the decay function over the decay interval.
 8. The methodof claim 7, wherein the decay function is a dual exponential function(DEF).
 9. The method of claim 8, wherein the dual exponential function(DEF) is expressed as:DEF=A _(BH)*exp(−t/τ_(BH))+A _(F)*exp(−t/τ _(F)), where A_(BH) and A_(F)are coefficients, t is time, τ_(BH) is a borehole decay constant, andτ_(F) is a formation decay constant.
 10. The method of claim 9, whereinthe borehole thermal neutron capture cross section is determined basedon τ_(BH).
 11. A system for measuring a porosity of an earth formationtraversed by a wellbore, the system comprising: a logging toolcomprising: a neutron source configured to emit neutrons into theformation at an energy sufficient to induce inelastic scattering gammarays and thermal capture gamma rays in the formation, a proximal gammadetector spaced a first axial distance from the neutron source, and afar gamma detector spaced a second axial distance from the neutronsource, and a computer configured to: receive data generated by thelogging tool, wherein the data indicates gamma rays detected at theproximal gamma detector and gamma rays detected at the far gammadetector, from the data, determine a count of thermal capture gamma raysdetected at the proximal gamma detector and a count of thermal capturegamma rays detected at the far gamma detector, determine aproximal-to-far thermal capture ratio as a ratio of the count of thermalcapture gamma rays detected at the proximal gamma detector to the countof thermal capture gamma rays detected at the far gamma detector,determine a borehole thermal neutron capture cross section, anddetermine the porosity from the proximal-to-far thermal capture ratioand the borehole thermal neutron capture cross section.
 12. The systemof claim 11, wherein determining the porosity comprises using theborehole thermal neutron capture cross section to compensate forborehole salinity.
 13. The system of claim 11, wherein the dataindicating the gamma rays detected at the proximal gamma detector andthe gamma rays detected at the far gamma detector comprises, for eachdetector, a time spectrum comprising a burst interval indicating gammaray counts detected while the neutron source is emitting neutrons and adecay interval indicating gamma ray counts detected while the neutronsource is not emitting neutrons.
 14. The system of claim 13, whereindetermining the count of thermal capture gamma rays detected at theproximal gamma detector and the count of thermal capture gamma raysdetected at the far gamma detector comprises, for each detector:determining a count of thermal capture gamma rays detected during thedecay interval at that detector, and determining a count of thermalcapture gamma rays detected during the burst interval at that detector.15. The system of claim 14, wherein determining a count of thermalcapture gamma rays detected during the decay interval comprisesintegrating the time spectrum over the decay interval.
 16. The system ofclaim 14, wherein determining a count of thermal capture gamma raysdetected during the burst interval comprises: fitting a decay functionto the decay interval of the time spectrum, determining a boreholecomponent and a formation component of the decay function over the decayinterval, convolving the borehole component and the formation componentof the decay function over the burst interval, and summing the convolvedborehole component and the convolved formation component over the burstinterval to determine the count of thermal capture gamma rays detectedduring the burst interval.
 17. The system of claim 11, whereindetermining the borehole thermal neutron capture cross sectioncomprises: fitting a decay function to the decay interval of the timespectrum, and determining a borehole component and a formation componentof the decay function over the decay interval.
 18. The system of claim17, wherein the decay function is a dual exponential function (DEF). 19.The system of claim 18, wherein the dual exponential function (DEF) isexpressed as:DEF=A _(BH)*exp(−t/τ _(BH))+A _(F)*exp(−t/τ _(F)), where A_(BH) andA_(F) are coefficients, t is time, τ_(BH) is a borehole decay constant,and τ_(F) is a formation decay constant.
 20. The system of claim 19,wherein the borehole thermal neutron capture cross section is determinedbased on τ_(BH).